COMMUNICATIONS TO THE EDITOR
Sept. 5, 1964
3563
I
Fig. 2.-Plot
of the 0 2 intercepts I - l ( O ) vs. A T .
techniques used in these experiments, we feel that the deviations are real and throw some doubt on the universal validity of the 0 2 and Debye theories. This conclusion stands in contrast to that of Miinster and Schneeweiss," who feel that a general conclusion as to the failure of the 02 theory cannot be drawn from the available evidence. In spite of the observed deviations, the Debye theory furnishes a very good approximation, and allows the calculation of meaningful parameters, namely the "radius of action of intermolecular forces" 2 and the correlation length L. The former may be calculated from eq. 1. of ref. 2b, and the latter from
I
02
0.1
Q
Fig. 3.-Plot
I
0.3
of the correlation length L us. A T .
An average 1 value of 8.7 f 1.0 8.is obtained from the seven temperature runs of Fig. 1. L is shown as a function of AT in Fig. 3. The suggestion that the deviations from the Debye and 0 2 theories occur for systems with abnormally flat consolute curves does not seem to hold." A more likely situation is that the 02 curves are not in fact linear except over a relatively narrow range of sin (8/2)/X; this is supported by our X-ray and light scattering observation for the nitrobenzene-n-heptane s y ~ t e mand , ~ ~also ~ by observations reported by Debye. l 2 Acknowledgment.-The authors are grateful to the National Science Foundation for supporting this research under NSF Grant G-19282.
(11)
A. Monster
and Ch. Schneeweiss, 2. physik. Chcm., S7, 369 (1963).
(12)
P. Debye, ref. 6,pp.
393-401
COMMUNICATIONS T O THE EDITOR Thermodynamic Properties of Nonpolar Mixtures of Small Molecules Sir : The treatment of n-paraffin hydrocarbons and their mixtures presented elsewhere in this (these papers will be referred to as I and 11, respectively) can be recast in a form* which appears to be generally (1) P. J. Flory, R. A. Orwoll, and A. Vrij. J. A m . Chcm. SOL.,8 8 , 3507 (1964). (2) P.J. Flory, R. A. Orwoll, and A. Vrij, ibid., 88, 3515 (1964). (3) P.J. Flory, to be published.
applicable to liquid solutions, irrespective of the size and shape of the molecular species, provided that they are not hydrogen bonded or highly polar. Here we present a preliminary comparison of theory with experiment for several representative binary mixtures of small, approximately spherical molecules. The enthalpy of mixing can be expressed as follows
COMMUNICATIONS TO THE EDITOR
3564
Molar volumes v, thermal expansion coefficients a, and thermal pressure coefficients y = (dp/bT)v for the pure components whose binary mixtures are considered here are listed in Table I. The reduced volumes 6, the characteristic temperatures T*, and the characteristic pressures p * , all calculated from the aforementioned equation of state parameters as prescribed in I, are given in this table also. Calculation of the excess functions for a given binary mixture according to the foregoing equations requires the single parameter xi2 in addition to the quantities characterizIna the Dure comDonents (Table f). Values chosen for Xy2 to afford opiimum agreement with the observed quantities are given in the first 'Ow Of 'I. In succeeding rows of Table 11, the calculated excess quantities for four equimolar mixtures are compared
TABLE I PARAMETERS FOR THE PURE COMPONENTS ca-c-CaHir CaH6 C(CH~),
---
'
v cc mole
X 101 deg - 1 ?, c a ~cc I deg (I
U
T*, " K . p*, cal. cc. - 1
-1
00
25'
250
250
94 I 191' o 3209d 1 2660 4571 140 4
97 O8 1 229" o 27276 1 2927 4697 135 8
lo8 75 1 217* 0 25530
89 40 1 223' o 3018e 1 2916 4708 150.0
1.2905 4719 126 7
Vol. 86
250
O3
1 811'
0 1.3687 3762 94.7
a S. E. Wood and J . A. Gray, J . A m . Chem. SOC., 74,3729 (1952). S. E. Wood and J . P. Brusie, ibid., 65, 1891 (1943). c American Petroleum Institute cornDilations. F. D. Rossini. el el., "Selected Values of Physical and'Thermodynamic Properties of Hydrocarbons and Related Compounds," API Research Project 44, Carnegie Press, Pittsburgh, Pa., 1953. Calculated from compressibilities reported by J , Jeener, J , Chem, P h y s , 25, 584 (1956) e Calculated from compressibilities reported by G . A . Holder and E. Whalley, T Y UFaraday ~ SOC.,58, 2095 (1962).
6
TABLE I1 COMPARISON OF CALCULATED A N D OBSERVED EXCESSQUANTITIES FUR EQUIMOLAR MIXTURES CCId(1) -c-CaHm(Z) 25'
CaHa(l)-CClr(Z) 250
__--_
,_--
X nvi*/R,
53 Calcd
0 0013 29 22
8"
H E I N , cal mo1e-I G E / N , cal mole-'
47 Obsd.
Calcd
0 0021 35 17
0 0011 26 19
In eq. 1 N1and N z are the numbers of moles and vl* and vz* are the characteristic molar volumes of species 1 and 2 (vi* = niv* in the notation of I and 11) po =
NZV2*/(N1Vl*
+ Nzvz*)
and Xlz is the pair interaction parameter (analogous but not equal to pl2*of eq. 11-24) defined formally by XI2 = s1()111
+
v22
- 2)112)/2(v1*)2
with s1 interpreted as the number of interaction sites per molecule of 1. We do not, however, make use of this relationship; Xl2 will be treated as an empirical parameter. Other quantities appearing in eq. 1 and 2 are defined in I and 11. For molecules differing considerably in size, the volume fraction pa should be replaced in eq. 1 by the corresponding surface (site) fraction; the distinction is unimportant however for the systems considered here. For spherical molecules of comparable size, the combinatorial term in eq. 11-14 for the free energy of mixing may be replaced appropriately by the ideal free energy. On this basis, the excess free energy can be written
+
( N z ~*v2 z */Tz*) In
[(a,"'
- l)/(d"'
- l)])
+ HE
0 0001 26 20
0 0063 146 107
0.0085 200 78
CClr(l)-C(CH>),(Zj 00 151
Calcd.
Obsd.
- 0.0095
- 0.0062
75 75
75 76
with experimental results. The latter are from the compilations included by Rowlinson. Calculations were carri5d out in the following way. The reduced temperature T = T/T* for each equimolar mixture listed in Table I1 was obtained from T* calculated according to eq. 4. The corresponding reduced volume d was then computed according to eq. 1-18 (see also eq. 11-12). Comparison with the ~ Z O Zgives the additive reduced volume do = pld1 calculated excess reduced voume iiE (Table 11). The excess enthalpies H E / N per mole of mixture were computed according to eq. 1, the calculated values of d being used. The excess free energies were computed according to eq. 3, the calculated values of H E I N and d being used for this purpose. Thus, [ ( H E - GE)/ T N I c a l c d as deduced from Table I1 represents the calculated excess entropy S E / N per mole of mixture. For two of the systems, dE is small and positive; for the third it is substantially positive, and for the last it is decidedly negative. Calculated CE values reproduce these variations fairly well. The significance of this achievement is underscored by the fact that neither the excess enthalpies nor the interaction parameters XI2 parallel the excess volumes. I t becomes apparent from examination of the relevant equations that a large difference between the characteristic temperatures T1* and T2* favors BE < 0, a tendency opposed by Xlz > 0. The comparisons presented are typical of those for other binary mixtures currently under investigation The calculated excess enthalpies match experiment within probable limits of error. It will be apparent from the data in Table I1 that the calculated excess entropies ( H E - GE)/Til: are in the direction of those observed.
+
(2)
GE = 3T{(Nipi*vI*/Ti*) In [(a,"' - 1)/(d'I3 - I ) ]
Obsd.
CsHa(Ij-c-CaH>r(2) 250 K 253 ~. Calcd. Obsd.
(3)
The term in braces represents, of course, the contribution from the excess entropy, and this contribution depends on equation of state properties of the pure components. The characteristic temperature T* for the mixture is given by
(4) J . S . Rowlinson, "Liquids and Liquid Mixtures," Butterworths, London, 19.59. References to original sources from which the data were obtained are given by Rowlinson.
Sept. 5, 1964
3565
COMMUNICATIONS TO THE EDITOR
A full treatment of the subject, including analysis of data for a wider variety of binary systems, will be published in the near f ~ t u r e . ~ Acknowledgment.-Support of the United States Air Force under Contract AF 49(638)-1341 is gratefully acknowledged.
CH~-C-CHz-C-CHzNHz I I CH3 I
HI
(5) A. Abe and P . J. Flory, in preparation.
DEPARTMENT OF CHEMISTRY STANFORD UNIVERSITY STANFORD, CALIFORNIA RECEIVED JUNE8 , 1964
P. J. FLORY A. ABE
The Reaction of Organoboranes with Chloramine and with Hydroxylamine-0-sulfonic Acid. A Convenient Synthesis of Amines from Olefins via Hydroboration
Sir:
8"* Representative results are summarized in Table I. TABLEI CONVERSION OF OLEFINS INTO AMINES B Y THE HYDROBORATION-ANIMATION REACTION
We wish to report that organoboranes, such as are -Yield, yoproduced in the hydroboration of representative oleHydroxylarnine-0fins,' react readily with either chloramine or with Chlorsulfonic hydroxylamine-0-sulfonic acid to form the correOlefin Amine acid amine sponding amine. I n the majority of cases examined, 1-0ctene n-Octylamine 64 yields of 60y0 ( + 5 % ) have been realized. Conse1-Decene n-Decylamine 51 quently, this procedure permits a simple conversion 2-Methyl-1-pentene 2-Methyl-1-amino59 29 of olefinic derivatives in to the corresponding amine. pentane 2,4,4-Trimethyl-l2,4,4-Trimethyl-l58 28 In the procedure the olefin in tetrahydrofuran solupentene arninopentane tion is conveniently converted into the corresponding a-Methylstyrene 2-Phenyl-1-amino58 58 organoborane by treatment with the equivalent propane quantity of diborane in tetrahydrofuran solution.2 I n 1,l-Diphenylethylene 8,p-Diphenylethyl27 the chloramine route, the organoborane, with added amine alkali, is treated with a freshly prepared solution of Cyclopentene Cyclopentylamine 59 50 chloramine3 for 1 hr. a t room temperature. In the Cyclohexene Cyclohexylamine 55 49 hydroxylamine-0-sulfonic acid procedure the reagent4 1-Methylcyclohexene trans-2-Methyl8.5 is added directly to the tetrahydrofuran solution and cyclohexylamine the reaction mixture heated under reflux for 3 hr. Norbornene eso-Norbornylamine 52 51 8-Pinene cis-Myrtanylamine 55 In both procedures the solutions are acidified with 48 Ethyl undecenoate 11-Aminoundecanoic 30 30 hydrochloric acid, extracted with ether to remove reacid sidual organoboron derivatives, and the amines are then isolated from the acidic aqueous solutions by standard The observation that the yields in so many cases methods. were in the range of 55 to 6070 suggested the possiThe yields are similar in both procedures. Howbility that only two of the three alkyl groups on the ever, the commercial availability of hydroxylamineorganoborane were undergoing reaction. This was 0-sulfonic acid avoids the synthesis and standarization confirmed by the isolation of the monoalkylboronic of the chloramine solution. Consequently, the use acid from the reaction mixture and the demonstration of the hydroxylamine-0-sulfonic acid is preferable in that the reaction of such boronic acids with the reagents cases where the reagent is available. is very slow. The hydroboration of hindered olefins I n this way 1-octene has been converted into n-octylproceeds readily only to the mono- or dialkylborane amine, a-methylstyrene into 2-phenyl-l-aminopropane, stage.' Consequently, the yields are much lower and 2,3,3-triniethyl-l-penteneinto 2,3,3-trimethyl- for such derivatives. In spite of the low yield realized 1-aminopentane (1). Similarly, cyclopentene and cyin applying the reaction to 1-methylcyclohexene, i t clohexene have been converted into the corresponding is of considerable theoretical interest that the product amines, and norbornene into em-norbornylamine (2). produced was pure trans-2-methylcyclohexylamine, The mildness of the procedure is indicated by the concorresponding to replacement of the boron by the version of &pinene into cis-myrtanylamine (3), withamino group stereospecifically with retentioil of conout evidence of any rearrangement or alteration of figuration. Similarly, the isolation of pure exothe carbon skeleton. norbornylamine supports the conclusion that the reaction course is stereochemically similar to that proposed ( 1 ) For a recent summary, see H . C . Brown, "Hydroboration." W. A . Benjamin, I n c , New York. N Y . , 1962. for the oxidation of the organoborane by alkaline ( 2 ) One molar solutions of borane in tetrahydrofuran are now commerhydrogen peroxide. cially available from Metal Hydrides Incorporated, Beverly, Mass. (3) T h e chloramine solution is prepared by treating dilute aqueous a m The following procedures are representative F . Raschig, Bcr., 40, 4586 (1907). monia with sodium hypochlorite a t 0' In a 500-ml. flask was placed 11.8 g. (100 mrnole:j ( 4 ) Hydroxylamine-0-sulfonic acid i s now commercially available from of a-methylstyrene and 30 ml. of tetrahj.!r3:u r m . Allied Chemical C o . , Marcus Hook, Pa. 7
